Structural interpretation of matched pole-zero discretisation

Deals with matched pole-zero discretisation, which has been used in practice for hand calculations in the digital redesign of continuous-time systems but available only in the transfer-function form. Since this form is inconvenient for characterising the time-domain properties of sampled-data loops and for computerising the design of such systems, a state-space formulation is developed. Under the new interpretation, the matched pole-zero model is shown to be structurally identical to a hold-equivalent discrete-time model, where the generalised hold takes integral part, thus unifying the most widely used discretisation approaches. An algorithm for obtaining the generalised hold function is presented. The hold-equivalent structure of the matched pole-zero model clarifies several discrete-time system properties, such as controllability and observability, and their preservation or loss with a matched pole-zero discretisation. With the proposed formulation, the matched pole-zero, hold-equivalent, and mapping models can now all be constructed with a single schematic model